Fabregas made what is thought to be his final Chelsea appearance on Saturday as the Blues beat Nottingham Forest 2-0 to progress to the fourth round of the FA Cup.
The Spain legend is out of contract at the end of the season and is close to agreeing a deal to join Ligue 1 outfit Monaco in January.
An emotional Fabregas missed a penalty against Nottingham Forest but nonetheless received a standing ovation at Stamford Bridge as he left the field.
Asked what Fabregas means to Chelsea following the game, Hazard said: Everything.
In five years I can say that I was lucky to play with him. Since the beginning when he came we won the double together.
Top guy on the pitch and off the pitch. A great friend of mine. I just have admiration for this guy.
I hope he will have a good future. He is still a very good player. He will enjoy it.
Asked whether Fabregas had indeed made his last Chelsea appearance, Blues coach Carlo Cudicini said: We dont know.
If it was his last game I think it was very good he played in front of his fans and he was able to get a nice reception.
What can I say about Cesc? He is a top player, a player who is unique in his position. He has unbelievable vision and awareness of where his team-mates are on the pitch.
Hes one of the few who has the ability to play that ball for the runs behind the defensive line, so precise and with the right timing – hes one of a kind.
Hes been fantastic for teams before us and the contribution hes given to this club and this team has been amazing.